Space-time asymptotics of the two dimensional Navier–Stokes flow in the whole plane
Space-time asymptotics of the two dimensional Navier–Stokes flow in the whole plane
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全平面二维纳维-斯托克斯流的时空渐近
DOI：
10.1016/j.jde.2017.09.025
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发表时间：
2018
影响因子：
2.4
通讯作者：
T. Okabe
中科院分区：
文献类型：
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作者：
T. Okabe
我们考虑二维Navier-Stokes流的时空行为。通过引入初始数据的定性结构，成功地导出了L1（R2）<$L σ 2（R2）中不带矩条件的Navier-Stokes流的一阶渐近展开式.此外，我们刻画了Miyakawa-Schonbek [21]提出的当t→∞时能量快速衰减的充要条件<$u（t）<$2 = o（t− 1）。通过在哈代空间中的加权估计，讨论了在初值满足一阶矩条件下，Navier-Stokes流的二阶渐近展开的可能性。此外，考虑到Navier-Stokes流u（t）在哈代空间H1（R2）中（t> 0），我们考虑了它的Hardy模渐近展开式.最后我们考虑了当t→∞时的快速时间衰变<$u（t）<$2 = o（t− 3 2），并引入了Brandolese [2]的循环对称性.
We consider the space-time behavior of the two dimensional Navier–Stokes flow. Introducing some qualitative structure of initial data, we succeed to derive the first order asymptotic expansion of the Navier–Stokes flow without moment condition on initial data in L 1 (R 2)∩ L σ 2 (R 2). Moreover, we characterize the necessary and sufficient condition for the rapid energy decay‖ u (t)‖ 2= o (t− 1) as t→∞ motivated by Miyakawa–Schonbek [21]. By weighted estimated in Hardy spaces, we discuss the possibility of the second order asymptotic expansion of the Navier–Stokes flow assuming the first order moment condition on initial data. Moreover, observing that the Navier–Stokes flow u (t) lies in the Hardy space H 1 (R 2) for t> 0, we consider the asymptotic expansions in terms of Hardy-norm. Finally we consider the rapid time decay‖ u (t)‖ 2= o (t− 3 2) as t→∞ with cyclic symmetry introduced by Brandolese [2].